In the vertebrate nervous system, activation of the N-methyl-D-aspartate (NMDA) glutamate receptor on neurons plays an important role in excitatory synaptic transmission, developmental and synaptic plasticity, and neurotoxicity. NMDA receptor activation can also lead to the production of the free radical nitric oxide (NO). Recent experiments suggest that NO production is necessary for synaptic plasticity in the mammalian cerebellum, hippocampus, and cortex. In the hippocampus, the conjunction of presynaptic activity and elevated NO or carbon monoxide (CO) levels potentiates transmission at active presynaptic terminals and leaves inactive terminals unaffected. NO production is also implicated in neurotoxicity, synchronization of neural activity leading to kindling, the control of general cerebrovascular tone, the coupling of local changes in neural activity to local changes in blood flow, and changes in neurotransmitter release. Importantly, NO is a potent vasodilatory substance, hence, mechanisms of synaptic plasticity that employ signals like NO link events associated with learning and synaptic plasticity to pathological states involving blood flow and seizures. Therefore, it is important to understand the computational properties of learning mechanisms that utilize rapidly diffusible signals like NO or CO. Since both CO and NO are membrane permeant gases, they are not restricted to their synapse of origin, rather, they act as volume signals that potentially influence synaptic function throughout a local volume of neural tissue. This fact opens exciting possibilities for the function of the vertebrate brain since standard models of neural transmission and plasticity will have to change to incorporate the ability of one synapse to pass information to another synapse whether or not they innervate the same postsynaptic cell. Additionally, a plasticity mechanism that utilizes membrane-permeant, rapidly diffusible substances would permit associations between afferent inputs to develop in local volumes of neural tissue, hence, this kind of learning mechanism has been called volume learning. There are two long-term goals of this project: 1) To elucidate the theoretical underpinnings of these new forms of neural communication and plasticity, and 2) to understand how such mechanisms would act during both activity-dependent development and learning. We will investigate the theoretical and computational consequences of using membrane permeant, rapidly diffusible signals to modulate synaptic plasticity and transmission. A particular emphasis will be placed on how the exact three dimensional relationships among synaptic contacts influences the production and action of the rapidly diffusible signals described above. This emphasis places a premium on the three dimensional dendritic morphology of postsynaptic neurons since this structure provides the scaffold on which the diffusive signals originate.